Which of the following numbers is a multiple of 13? ${40,78,82,93,103}$
Explanation: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $40 \div 13 = 3\text{ R }1$ $78 \div 13 = 6$ $82 \div 13 = 6\text{ R }4$ $93 \div 13 = 7\text{ R }2$ $103 \div 13 = 7\text{ R }12$ The only answer choice that leaves no remainder after the division is $78$ $ 6$ $13$ $78$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $78$ $78 = 2\times3\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $78$. We can say that $78$ is divisible by $13$.